7.84/3.58 MAYBE 9.72/4.09 proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs 9.72/4.09 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 9.72/4.09 9.72/4.09 9.72/4.09 H-Termination with start terms of the given HASKELL could not be shown: 9.72/4.09 9.72/4.09 (0) HASKELL 9.72/4.09 (1) BR [EQUIVALENT, 0 ms] 9.72/4.09 (2) HASKELL 9.72/4.09 (3) COR [EQUIVALENT, 0 ms] 9.72/4.09 (4) HASKELL 9.72/4.09 (5) NumRed [SOUND, 0 ms] 9.72/4.09 (6) HASKELL 9.72/4.09 (7) Narrow [COMPLETE, 0 ms] 9.72/4.09 (8) QDP 9.72/4.09 (9) NonTerminationLoopProof [COMPLETE, 0 ms] 9.72/4.09 (10) NO 9.72/4.09 9.72/4.09 9.72/4.09 ---------------------------------------- 9.72/4.09 9.72/4.09 (0) 9.72/4.09 Obligation: 9.72/4.09 mainModule Main 9.72/4.09 module Main where { 9.72/4.09 import qualified Prelude; 9.72/4.09 } 9.72/4.09 9.72/4.09 ---------------------------------------- 9.72/4.09 9.72/4.09 (1) BR (EQUIVALENT) 9.72/4.09 Replaced joker patterns by fresh variables and removed binding patterns. 9.72/4.09 ---------------------------------------- 9.72/4.09 9.72/4.09 (2) 9.72/4.09 Obligation: 9.72/4.09 mainModule Main 9.72/4.09 module Main where { 9.72/4.09 import qualified Prelude; 9.72/4.09 } 9.72/4.09 9.72/4.09 ---------------------------------------- 9.72/4.09 9.72/4.09 (3) COR (EQUIVALENT) 9.72/4.09 Cond Reductions: 9.72/4.09 The following Function with conditions 9.72/4.09 "undefined |Falseundefined; 9.72/4.09 " 9.72/4.09 is transformed to 9.72/4.09 "undefined = undefined1; 9.72/4.09 " 9.72/4.09 "undefined0 True = undefined; 9.72/4.09 " 9.72/4.09 "undefined1 = undefined0 False; 9.72/4.09 " 9.72/4.09 9.72/4.09 ---------------------------------------- 9.72/4.09 9.72/4.09 (4) 9.72/4.09 Obligation: 9.72/4.09 mainModule Main 9.72/4.09 module Main where { 9.72/4.09 import qualified Prelude; 9.72/4.09 } 9.72/4.09 9.72/4.09 ---------------------------------------- 9.72/4.09 9.72/4.09 (5) NumRed (SOUND) 9.72/4.09 Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero. 9.72/4.09 ---------------------------------------- 9.72/4.09 9.72/4.09 (6) 9.72/4.09 Obligation: 9.72/4.09 mainModule Main 9.72/4.09 module Main where { 9.72/4.09 import qualified Prelude; 9.72/4.09 } 9.72/4.09 9.72/4.09 ---------------------------------------- 9.72/4.09 9.72/4.09 (7) Narrow (COMPLETE) 9.72/4.09 Haskell To QDPs 9.72/4.09 9.72/4.09 digraph dp_graph { 9.72/4.09 node [outthreshold=100, inthreshold=100];1[label="minBound",fontsize=16,color="blue",shape="box"];14[label="minBound :: Char",fontsize=10,color="white",style="solid",shape="box"];1 -> 14[label="",style="solid", color="blue", weight=9]; 9.72/4.09 14 -> 3[label="",style="solid", color="blue", weight=3]; 9.72/4.09 15[label="minBound :: Bool",fontsize=10,color="white",style="solid",shape="box"];1 -> 15[label="",style="solid", color="blue", weight=9]; 9.72/4.09 15 -> 4[label="",style="solid", color="blue", weight=3]; 9.72/4.09 16[label="minBound :: Int",fontsize=10,color="white",style="solid",shape="box"];1 -> 16[label="",style="solid", color="blue", weight=9]; 9.72/4.09 16 -> 5[label="",style="solid", color="blue", weight=3]; 9.72/4.09 17[label="minBound :: Ordering",fontsize=10,color="white",style="solid",shape="box"];1 -> 17[label="",style="solid", color="blue", weight=9]; 9.72/4.09 17 -> 6[label="",style="solid", color="blue", weight=3]; 9.72/4.09 18[label="minBound :: ()",fontsize=10,color="white",style="solid",shape="box"];1 -> 18[label="",style="solid", color="blue", weight=9]; 9.72/4.09 18 -> 7[label="",style="solid", color="blue", weight=3]; 9.72/4.09 3[label="minBound",fontsize=16,color="black",shape="box"];3 -> 8[label="",style="solid", color="black", weight=3]; 9.72/4.09 4[label="minBound",fontsize=16,color="black",shape="box"];4 -> 9[label="",style="solid", color="black", weight=3]; 9.72/4.09 5[label="minBound",fontsize=16,color="black",shape="box"];5 -> 10[label="",style="solid", color="black", weight=3]; 9.72/4.09 6[label="minBound",fontsize=16,color="black",shape="box"];6 -> 11[label="",style="solid", color="black", weight=3]; 9.72/4.09 7[label="minBound",fontsize=16,color="black",shape="box"];7 -> 12[label="",style="solid", color="black", weight=3]; 9.72/4.09 8[label="Char Zero",fontsize=16,color="green",shape="box"];9[label="False",fontsize=16,color="green",shape="box"];10[label="primMinInt",fontsize=16,color="black",shape="triangle"];10 -> 13[label="",style="solid", color="black", weight=3]; 9.72/4.09 11[label="LT",fontsize=16,color="green",shape="box"];12[label="()",fontsize=16,color="green",shape="box"];13 -> 10[label="",style="dashed", color="red", weight=0]; 9.72/4.09 13[label="primMinInt",fontsize=16,color="magenta"];} 9.72/4.09 9.72/4.09 ---------------------------------------- 9.72/4.09 9.72/4.09 (8) 9.72/4.09 Obligation: 9.72/4.09 Q DP problem: 9.72/4.09 The TRS P consists of the following rules: 9.72/4.09 9.72/4.09 new_primMinInt([]) -> new_primMinInt([]) 9.72/4.09 9.72/4.09 R is empty. 9.72/4.09 Q is empty. 9.72/4.09 We have to consider all (P,Q,R)-chains. 9.72/4.09 ---------------------------------------- 9.72/4.09 9.72/4.09 (9) NonTerminationLoopProof (COMPLETE) 9.72/4.09 We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. 9.72/4.09 Found a loop by semiunifying a rule from P directly. 9.72/4.09 9.72/4.09 s = new_primMinInt([]) evaluates to t =new_primMinInt([]) 9.72/4.09 9.72/4.09 Thus s starts an infinite chain as s semiunifies with t with the following substitutions: 9.72/4.09 * Matcher: [ ] 9.72/4.09 * Semiunifier: [ ] 9.72/4.09 9.72/4.09 -------------------------------------------------------------------------------- 9.72/4.09 Rewriting sequence 9.72/4.09 9.72/4.09 The DP semiunifies directly so there is only one rewrite step from new_primMinInt([]) to new_primMinInt([]). 9.72/4.09 9.72/4.09 9.72/4.09 9.72/4.09 9.72/4.09 ---------------------------------------- 9.72/4.09 9.72/4.09 (10) 9.72/4.09 NO 9.85/4.13 EOF